Electrical multiplying and dividing machine



H. P. LUHN 2,566,947

ELECTRICAL MULTIPLYINC AND DIVIDINC MACHINE sept. 4, 1951 17 Sheets-Sheet 1 Filed Jam.l 16, 1948 001.6 FV canr cazz coz.)

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@lisa f 2 m ou 1. 11m L .1D .,a y T1* E .w E n nl Z .M 9 Z 0 m F fr, x: .R 40V L, M M 0 ma. a/w. Mb z/wf /M INVENTOR TEJLG- Sept. 4,A 1951 H. P. LUHN ELECTRICAL MULTIPLYING AND DIVIDING MACHINE Filed Jan. 1e. 194e 17 Sheets-Sheet 5 INVENTOR /f/H/VS P UH/V BY t f ATTORNEY H. P. LUHN `ELJEICTRICL MULTIPLYING AND DIVIDING MACHINE Filed Jan. 16. 1948 1'? Sheets-Sheet 4 slept. 4, 1951 PTU- ITE-J C CMM fw ATTORNEY 17 Sheets-Sheet 5 COU/V75? H. P. LUHN y ELECTRICAL MULTIPLYING lAND DIVIDING MACHINE Filed Jan.v 16. 1948 Sept. 4, 1951 :,r-f-/f ATTORNEY TE-li Sept. 4, 1951 H. P. L UHN 2,566,947

' ELECTRICAL MULTIPLYING AND DIVIDING MACHINE Filed Jan. 1e, 1948 17 sheets-sheet e NVENTOR ATTORNEY Sept 4, 1951 H. P. L UHN ELECTRICAL MULTIPLYING AND DIVIDING MACHINE Filed Jan. 16, 1948 17 Sheets-Sheet 7 LOA/e P Sept. 4, 1951 H. P. LUHN 2,566,947

ELECTRICAL MULTIPLYING AND DIVIDINGKMACHINE Filed Jan. 1e, 1948 l 1v sheets-sheet a INVENTOR ATTORN EY Sept. 4, 1951 H. P. LUHN ELECTRICAL mJLTIPLYING AND DIVIDING MACHINE Filed Jan; 16, v1948 17 Sheets-Sheet 9 -4'- INVENToR HHM? P (/H/V A BY t ATTORNEY j Sept. 4, 1951 H. P. Lul-1N ELECTRICAL MULTIPLYING AND DIVIDING MACHINE 17 Sheets-Sheet 10 Filed Jan. 16, 1948 X 479 275607 (Correct for L15/a2ac@ gaaf/en!) -655X49 726.592 (Complement) Sept. 4, 1951 I-I. P. LUI-IN ELECTRICAL MULTIPLYING AAND DIVIDING MACHINE 4 Filed Jan.' 1e. 1948 17 sheets-sheet 1s Egg/2 1 SHIFT ADD { ADD 21569 Pamuk {Ann 419 Dd In11 SHIFT ADD O PRODUCT 1 -EEG- INvENToR HANS P L 4L/liv BY l - ATTORNEY 17 Sheets-Sheet 14 H. P. LUHN ELECTRICAL MULTIPLYING AND DIVIDING MACHINE Sept. 4, 1951 Filed Jan. 16, 1948 Sept 4, 1951 H. P. LUHN ELECTRICAL MULTIPLYINC AND DIVIDINC MACHINE Filed Jan. 16. 1948 17 Sheets-Sheet 15 u Q u Q KN umw WN MN C A N uws INVENTOR P. LUH

HANS` BY i atentetll Sept. 4,

UNITED STATES rATENT OFFICE ELECTRICAL MULTIPLYING AND DIVIDING MACHINE Hans I'.Y Luhn, Armonk, N. `Y.,fassignor to `International. Business Machines Corporation, New

York, N ..Y.,. a .corporation of .New York Application January 16, 1948, Serial'No. 2,777

tiplication or division to robtain aproduct or .quotient respectively or which may :be `utilized vto perform combined multiplicationand division '-.to obtainthe result-of an expression A EXC' -Amorespecic object of the inventionvis .to provide a relay type of calculating mechanism responsive to a series ofV electrical impulses wherein each alternate impulse will eiiect an algebraic summation of values set up on the relays.

A further object of the invention residesvin Vthe provision of relay devices settable to :rep-

resenta dividend and a divisor ,and in which,:fin

response to a single electrical impulse, .aidetermination is made as to whether the dividendis equal to, less than, or greater than 11/2 times the divisor.

A still further object resides in theprovision of relay devices settable to representa dividend anda divisor and inwhich, inresponsefto a singleelectrical impulse, a determination is made as to whether the dividend is equal to. less than or greater than 1/2 the divisor.

Another object of the invention resides inthe provision of a novel comparing mechanismin which twov numbers may be set upwith Veither one in the form of a complement and theother in the form oi a true number, and in which in response to a single electrical impulse .therelative magnitude of one with respect to 11/2 .times the other is ascertained. Y

Another object of the invention resides .in the provision of a novel comparing mechanism vin which two numbers may be set upl with either yonein the form of a complement and the-other in the form of a true number, and in which in response to a single electrical impulse .therelative magnitude of one with respect to 1/2 .the other is ascertained.

A further object of the invention is toprovide a dividing mechanism of the over-andover subtraction type having columnshift devices controlled in accordance with the relative magnitude of the dividend with respect to 'l1/2 times the divisor.

Astill further object is toprovide a calculating `mechanismA of the relay 'type wherein a dividend is repeatedly reduced by the .divisor or a multiple thereof and in which a multiplier or va multiple thereof is concurrently and "correspondingly entered into an adding device to obtainv the sum thereof.

Another object of the invention-is to provide a set voifrelays in which a digit may be represented in combinationalform and in 'which a digit represented in decimal form may be entered by setting the reiays'to'represent the digits 0. l, 2, etc. in turn and interrupting the setting vafter a number of setting steps equal to the value "of the digit.

A further .object of the invention -is to providedan improved yrelay summation apparatus 'in which three sets of relays are provided,

amounts set up on two oi' the "sets are added, Aand entered into the third set in response toa single electrical impulse, and a second impulse will transfer the sum in the third set back to one vof the 'nrst two. The arrangement provides for A'maintaining the setting of the first two r`sets of 'relays until the retransi'er and then dropping out '."therelays not. required in the new setting. This Yresults in greater operating speed as no sepa- -rate yclearing step is necessary.

Anotherobject of the invention is to provide a single calculating apparatus in which two amounts `may be entered and in which .by the lsimple setting oi a single .switch the apparatus will obtain either the quotient of one .o the .amounts divided by the other or the product oi lthe two.

Other objects of the inventionwill be pointed out in the following descriptionand claims and illustrated in the accompanying drawings, which disclose. by way of example. the principle of the invention and the best mode, which `has'been contemplated, of applying that principle.

In the drawings: `Figs. .1, la, `1b, lc, ldand le arrangedverti- -callyin the order named constitute a wiring diagram ofthe electric circuits of the appara- Vtus.

Figs.2 and 3 placed's'ide by r'side constitute a The Fig-4 is a wiring diagram of one denominational order `of the comparison device rand in Fig.

l1c` it is represented by rectangles .to indicate that `several suchorders are provided and vinterconnected as shown.

Figs. 5 and 5a taken together illustrate graphically the settings of the several sets of relays throughout the succession of steps of operation involved in the solution of a combined multiplying and dividing problem.

Fig. 6 is a diagram illustrating the mathematical procedure involved in the solution of a problem of combined multiplying and dividing and also dividing solely.

Fig. 6a. is a similar diagram for multiplying alone.

Figs. 7a and 7b taken together constitute a timing diagram of the several relays and circuit closing devices involved in the sequence of operation during the solution of a, selected problem.

Figs. 8, 8a, 9, 9a are diagrams facilitating the explanation of the 1X2 comparison device.

Figs. 10, 10a, 10b and 10c are diagrams facilitating the explanation of the 11/2 comparison device.

General principles of operation In order to explain the sequence of operations, a specific problem will be taken and the various steps required to arrive at a solution will be set forth in detail in connection with the circuit diagram and the timing chart (Fig. 7a, 7b).

The problem chosen is In effect, the machine will divide 51s by v79a correct to a predetermined number of lplaces and attain the product of this quotient times the value 419, which is 273.607. The dividing operations are carried out by a modified form of over-and-over subtraction, and the multiplying operations are carried out by a modified form of over-and-over addition with the two computations taking place concurrently.

Referring to Fig. 6, the mathematical steps involved in the process are set forth for manual `computation and the several steps are identified by numbers along the left hand margin of the gure'. The first three steps designated 0, I I and I2 represent Ipreliminary steps taken by the machine to initially alignl the dividend 518 and the divisor 793 in the relationship indicated in step I3, which indicates that the divisor is to be substracted from the dividend. noted in this example that the divisor is larger than the dividend. In the usual form of overand-over subtraction method, this subtraction would be performed but a column shift would first be effected.

YIn accordance with the principles employed -in the present invention, the subtraction as indicated at step I3 is carried out algebraically to obtain the negative difference 275 at step I4. Before this subtraction is effected, the two factors are inspected or compared to determine whether the dividend is greater, equal to or less than 1/2 the divisor and also whether the dividend is greater, equal to or less than 11/2 times the divisor. Where, as in the present case, the dividend is greater than 1/2 the divisor but is less than 11/ the divisor, it is a signal that the indicated subtraction is to be performed algebraically and that a column shift of the divisor to the right is to follow, so that at step I4 the negative remainder which might be said to represent an overdraft is to have added thereto an increment representing .l0 of the divisor, (due to the column shift). The comparison at step I4 indicates that now the dividend is greater It will be than 11/2 the divisor and also obviously greater than 1/2 the divisor which is a signal that the algebraic addition is to occur without the subsequent column shift, so that at step I5 the overdraft has been reduced to 195.7 and a second reduction occurs, reducing it to 116.4 followed by a third reduction reducing the value `to 37.1.

It will be noted that this value 37.1 represents the dividend reduced by seven times the divisor with an overdraft of 37.1 and is the same result A that would have been attained by repeatedly subtracting 793 seven times with an initial column shift. It is apparent, therefore, that in accordance with the present method the divisor is first subtracted one unit and then added back .3 ofa unit with a net reduction of .7.

Inspection will show that, if the divisor were subtracted again with the preceding denominational relationship, the net result would be to reduce the dividend by 6 times the divisor with a positive remainder of 43.2. If this step is carried out, it would have to be followed by a column shift operation before further reduction could take place. With the present method the shift requirement is anticipated in the following manner. At step IS it is, determined that the dividend is greater than 1/2 the divisor but is less than 11/2 times, this being a condition similar to that for step I3 and calls for adding followed by a shift operation. The 1% comparison in effect discovers at this time that, when the algebraic summation occurs, the remainder must be such that a shift will be required. Therefore, it anticipates and calls for the shift so that at step I1 the divisor is shifted one further step to the right to reduce the dividend by .01 of the divisor. Comparison at this and the several following steps shows the dividend to be greater than 11/2 the divisor, so that according to the rule, algebraic summation takes place to repeatedly reduce the remainder 5 times, resulting in the value 2.55 at step 22. This is the same result that would have been obtained if the divisor had been subtracted 6 times with an initial column shift of 5 more times with a further column shift.

At step 2| the inspection again indicated the dividend to be greater than 1/2 the divisor but less than 11A. times the divisor and calls for a column shift after the summation, which is represented at step 22 and is followed by two more reducing operations to obtain the remainder .171 after a shift is called for by the comparison or inspection at step 24.

I 'In the foregoing manner, the dividend is reduced through algebraic summation determined by inspection of the factors, and following the simple rule that, whenever the dividend is greater than 11/2 times the divisor, summation occurs Without column shift and, where comparison indicates that the dividend is greater than 1/2 the divisor but less than 11/2 times the divisor (that is, it lies somewhere between these two values of 'the divisor), summation is to occur and to be followed by a column shift.

It may occur, due to the relationship of the values, that at some comparison step the dividend is found to be less than 1/ the divisor, in which case the column shift alone is called for as exemplified in the 0, II and I2 steps, so that after the initial factors have been aligned at step I3 the 'procedure thereafter will be in accordance with the three rules to bring about adding (algebraic 5 summation) with accompanying, shift:v adding alone; or shifting alone.-

In Fig. 6, the manner in which. the result 273.607 is obtained is indicated in the central column of figures, where the multiplier is initially positioned in correspondence with the positioning of the divisor and where the multiplier is accumulated additively for each subtraction of the divisor and subtracted for each addition of the divisor with corresponding column shifting. Thus, at step I3 the negative 793 has an accompanying positive 419 which added to results inr a value representing 419 times the. quotient digit 1.

After column shift at step I4, there is represented subtraction of 419 three times, at steps I4, I5 and I6 leaving the result at `step I'I of 293.30 which represents 419 timesthe quotient of .7o at this point with the negativeremainder cir-37.10. Subsequent column shift and subtraction of 419. five times at steps II, I8, I9, 20 andv 2I, results in 272.35 at step 22 which represents 419 times. the quotient .65 with the remainder 2.55, and; nnally after column shift andthreemore steps. the ultimate value 273.607 atl step. 25 represents the quotient .653 times 419 with the re,- mainder .171.

The right hand column of isuresin Fie. eA represents the corresponding steps with a multiplier ofy 1,l and it.4 will be noted from inspection that this will result in attaining the quotient .553 as such. It may be stated at this point in the operation Of, the machine,v wheres straight dividing operation is to be performed the multiplier is in effect given the value of l, so that the result then becomes the quotient.

Following a similar procedure, if the divisor is given the value of 1, the result will bethe product of what has been called the dividend times the multiplier. This is illustratedV in. Fig.. 6a where` the value l is substituted for the divisor 793 of Fig. 6 and from inspection and following the rules explained, it will be noted that multiplication involves `over-and-over subtraction of l from. one factor accompanied by over-and-over addition of the other until theiirst is reduced to zero. Column shift is anticipated when the reduced factor becomes less than 11/2 timesV 1000, 100 orlo as.

the case may be.

By means of the principlesfollowed, the same computing structure may. beY employed andwill operate in the same. manner to effect multiplying, dividing or combined multiplying and dividing.v

The. methody of computation va. applied to the machine Figs. 5 anda represent inadiagra-mmaticmanner sets of values entered into relays designated as A, B, C, Dand F relays which are arranged tol receive values and transfer them from, one set.

to anotherduring successive steps of operation,

of the machine. Thesestepsare identified along the left hand marginasbeginning with step designated 9 and continuing with 8, 1, etc., with sufficient steps provided to take care. of the requirements .for the chosen machine, capacity. The factors are derived from a data source in the form. of the well known perforated record card which is provided with columns and rows' of perforating positions as shown in Fig. 1. This card traverses sensing brushes I2 so that designations representing 9 are sensed at the 9 step or point in the cycle, those. representing 8 are sensed in the 8 time andso on.

j Referring back to Fig. 5, certain columnarV relay positions have X marked therein. This represents the point of time in the cycle at which a perforation is sensed in a related card column and effects an entry in the corresponding set of relays. Through circuits to be explained in detail, the C relays will receive impulsesin response to sensing of the divisor and multiplier values 793 and 419 respectively and through a system whereby values are transferred from the Ci relays to B relays and back again will setup these factors in the C relays at the 0 time in the cycle. Likewise, the D relays will receive the impulses from the card representing the dividend and through transfer back and forth with the A relays, will obtain the dividend 518 at the 0 time in the` cycle, which corresponds to the 0 timefin Fig. 6;

In the Voperation of the machine, each cycle or step of operation is divided into two parts designated the a and b parts, and provision is made for emitting impulses during the a part and during the b part which will hereinafter be designated a and o impulses. These impulses are directed through the circuit network to effect transfer of data from one set of relays to another; to effect summation of data standing in the A and B relays.; to effect comparison between the data standing in the A relays and that standing in the B and C relays; and other incidental functions which will be pointed out as the explanation progresses.

After the factors are set up in the C and D relays, the machine will automatically and sequentially go through the mathematical steps explained in connection with Fig. 6. In handling the values, however, advantage is taken-of the convenience offered in handling some of the values in their complementary form and in the chart Fig. 5 the complementary values are represented as they are set on the various sets of relays.

Referring particularly to the 0 step, it is indicated by an oblique arrow that the dividend 518 is transferred to the A relays in the position shown and concurrently (in response to a b impulse) the divisor 793 and multiplier 419 are transferred from the C relays to the B relays in the form of 9s complements. Along line a of step Il is indicated that the summation of the amount in the A and B relays takes place with the result set up in the D relays, but this is in effect an idle operation. It is also indicated along the a line of step II that a comparison takes place, which indicates that the dividend is less than 1/2 the divisor and therefore calls for av shiftl Without summation. At the same time, the dividend value 518 is transferred from the A relays to the F relays from which it is transferred back to the A relays at the b time in step II with a column shift toward the left.

At this point it is to be particularly noted, that in handling the values in the machine, insteady of (as explained in connection with Fig. 6) shifting the divisor toward the right as is more` cus-,- tomary, the dividend is shifted toward the left with the same relative effect.

Accompanying the shifted entry at the b time in step II, the divisor and multiplier areagain.

entered in the B relays in complementary form; and, since the comparison is the same as before,

summation into the D relays is again effected with the dividend transferred to the F relays, and thence back to the A relays with another column'V shift. This procedure is repeated until at the a." 

